Lagrangian trajectory models have been demonstrated to be a useful tool in oil spill response. Despite the improvements in this kind of models, surface drift prediction remains a difficult task plagued with uncertainties. This work presents a Stochastic Lagrangian Trajectory Model (SLTM) that quantifies the uncertainties in trajectory simulations and defines the most likely search area of possible trajectories. The methodology includes the following steps: 1) Numerical scheme based on the transport equation in Lagrangian form; (2) Parameter estimation process, which includes: (i) time independent parameter estimation based on the maximum likelihood method and (ii) time dependent parameter estimation through autoregressive moving average; (3...